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The objective of the present study was to evaluate the association between the expression of sperm mannose-ligand receptors and sperm morphology. Sperm samples were obtained from 45 men, 30 fertile sperm donors and 15 infertile men. Sperm concentration, motility and morphology were evaluated and then incubated with control medium (Ham's F-10 + 1% HSA) for 4 h. Expression of mannose-ligand receptors was evaluated by mannosylated-BSA-FITC (subdivided into 3 patterns: I, for uncapacitated sperm; II, for capacitated; and III, for acrosome-reacted sperm). The mean ( ±SE) frequencies of sperm cells of the total sperm population that expressed patterns I, II, and III were 88 ±2.1%, 7 ±1.6%, and 5 ±0.8%, respectively, for fertile men, and 90 ±2.1%, 7 ±1.3%, and 3 ±0.5%, respectively, for infertile men. The rate of pattern III expression of mannose-ligand receptors was significantly higher in the fertile group compared to the infertile patients ( p < .01). A poor but significant correlation was observed between the rate of pattern III and the percentage of normal-forms sperm cell in the ejaculate ( r = .35, p = .018). Fertile sperm samples express more advanced patterns of mannose-ligand receptors compared to infertile men. This phenomenon is related to the morphology of human sperm cell in the ejaculate more than to any other basic sperm characteristics.

Let $\mathcal{A}_n $ denote a random acyclic directed graph which is obtained from a random graph with vertex set $\{ 1,2, \cdots ,n\} $, such that each edge is present with a prescribed probability pand all the edges are directed from higher to lower indexed vertices. Define a subset of vertices in $\mathcal{A}_n $ to be strongly independent if there is no directed path between any pair of vertices in the subset. We show that the sequence $\mathcal{J}(\mathcal{A}_n )$, the number of vertices in the largest strongly independent vertex subset of $\mathcal{A}_n $ satisfies with probability tending to 1, \[ \frac{\mathcal{J} (\mathcal{A}_n )}{\sqrt{\log n}} \to \frac{\sqrt{2 }}{\sqrt{\log 1/q}}\quad {\text{as}}\,n \to \infty , \] where $q=1-p$.